Explicit physics instruction
This investigation tests angular–linear consistency using supplied or simulated data.
Use a turntable/wheel simulation or supplied rotation dataset. Track angular position and two radii; compare predicted and measured linear speeds.
Preserve raw time/angle/radius data before calculating ω or v.
Core relations: s=rθ; v=rω; a_t=rα.
Worked example
At r=0.20 m and ω=5 rad/s, v should be 1.0 m/s; compare this prediction with the simulated point speed.
Guided question
Which measured quantities are required to test v=rω?
Independent work
- Preserve a raw time–angle table.
- Calculate ω over at least three intervals.
- Predict v at two radii.
- Compare prediction with simulation and record one residual/uncertainty.
Investigation / Data Lab
Use a turntable/wheel simulation or supplied rotation dataset. Track angular position and two radii; compare predicted and measured linear speeds.
Evidence record: raw data, calculations, graph, uncertainty, and one revision.
Misconception check
Same angular speed does not mean same linear speed for points at different radii.
Formative check
What quantity must be known, in addition to ω, to determine a point’s linear speed?
Reveal response
Its distance r from the rotation axis.
Mentor evidence conference
Ask Archaemenes to audit radians, graph interpretation, radius dependence, and unit consistency.
Teacher guidance
Foundation: Identify θ, ω, α and use one-step relations.
Core: Connect angular graphs with linear speed.
Extended: Analyze residuals and compare points at multiple radii.